Spectral Energy Flux Research Articles

Transient Tropopause Waves

Abstract Flight-level airborne observations have often detected gravity waves with horizontal wavelengths near the tropopause. Here, in situ and remote sensing aircraft data of these short gravity waves trapped along tropopause inversion layer and collected during a mountain-wave event over southern Scandinavia are analyzed to quantify their spectral energy and energy fluxes and to identify nonstationary modes. A series of three-dimensional numerical simulations are performed to explain the origin of these transient wave modes and to investigate the parameters on which they depend. It turns out that mountain-wave breaking in the middle atmosphere and the subsequent modification of the stratospheric flow are the key factors for the occurrence of trapped modes with . In particular, the intermittent and periodic breaking of mountain waves in the lower stratosphere forms a wave duct directly above the tropopause, in which the short gravity waves are trapped. The characteristics of the trapped, downstream-propagating waves are mainly controlled by the sharpness of the tropopause inversion layer. It could be demonstrated that different settings for optimizing the numerical solver have a significantly smaller influence on the solutions.

Probing the Nonlinear Interactions of Supertidal Internal Waves Using a High-Resolution Regional Ocean Model

Abstract The internal wave (IW) continuum of a regional ocean model is studied in terms of the vertical spectral kinetic energy (KE) fluxes and transfers at high vertical wavenumbers. Previous work has shown that this model permits a partial representation of the IW cascade. In this work, vertical spectral KE flux is decomposed into catalyst, source, and destination vertical modes and frequency bands of nonlinear scattering, a framework that allows for the discernment of different types of nonlinear interactions involving both waves and eddies. Energy transfer within the supertidal IW continuum is found to be strongly dependent on resolution. Specifically, at a horizontal grid spacing of 1/48°, most KE in the supertidal continuum arrives there from lower-frequency modes through a single nonlinear interaction, whereas at 1/384° and with sufficient vertical resolution KE transfers within the supertidal IW continuum are comparable in size to KE transfer from lower-frequency modes. Additionally, comparisons are made with existing theoretical and observational work on energy pathways in the IW continuum. Induced diffusion (ID) is found to be associated with a weak forward frequency transfer within the supertidal IW continuum. ID is also limited to the highest vertical wavenumbers and is more sensitive to resolution relative to spectrally local interactions. At the same time, ID-like processes involving high-vertical-wavenumber near-inertial and tidal waves as well as low-vertical-wavenumber eddy fields are substantial, suggesting that the processes giving rise to a Garrett–Munk-like spectra in the present numerical simulation and perhaps the real ocean may be more varied than in idealized or wave-only frameworks.

Nonlinear mode coupling and energetics of driven magnetized shear-flow turbulence

To comprehensively understand the saturation of two-dimensional (2D) magnetized Kelvin–Helmholtz-instability-driven turbulence, energy transfer analysis is extended from the traditional interaction between scales to include eigenmode interactions, by using the nonlinear couplings of linear eigenmodes of the ideal instability. While both kinetic and magnetic energies cascade to small scales, a significant fraction of turbulent energy deposited by unstable modes in the fluctuation spectrum is shown to be re-routed to the conjugate-stable modes at the instability scale. They remove energy from the forward cascade at its inception. The remaining cascading energy flux is shown to attenuate exponentially at a small scale, dictated by the large-scale stable modes. Guided by a widely used instability-saturation assumption, a general quasi-linear model of instability is tested by retaining all nonlinear interactions except those that couple to the large-scale stable modes. These complex interactions are analytically removed from the magnetohydrodynamic equations using a novel technique. Observations are an explosive large-scale vortex separation instead of the well-known merger of 2D, a dramatic enhancement in turbulence level and spectral energy fluxes, and a reduced small-scale dissipation length scale. These show the critical role of the stable modes in instability saturation. Possible reduced-order turbulence models are proposed for fusion and astrophysical plasmas, based on eigenmode-expanded energy transfer analyses.

Wave Buoy Measurements at Short Fetches in the Black Sea Nearshore: Mixed Sea and Energy Fluxes

Wave buoy measurements were carried out near the northeastern Black Sea coast at the natural reserve Utrish in 2020–2021. In total, about 11 months of data records were collected during two stages of the experiment at 600 and 1500 m offshore and depths of 18 and 42 m. The measured waves propagate almost exclusively from the seaward directions. Generally, the waves do not follow the local wind directions, thus, implying a mixed sea state. Nevertheless, dimensionless wave heights and periods appears to be quite close to the previously established empirical laws for the wind-driven seas. The results of the wave turbulence theory are applied for estimates of spectral energy fluxes and their correspondence to the energy flux from the turbulent wind pulsations. These estimates are consistent with today’s understanding of wind–wave interaction. It is shown that the main fraction of the wind energy flux is sent to the direct Kolmogorov–Zakharov cascade to high wave frequencies and then dissipates in small amounts. Less than 1% of the wind energy flux is directed to the low frequency band (the so-called inverse Kolmogorov–Zakharov cascade), thus, providing wave energy growth.

Spectral Kinetic-Energy Fluxes in the North Pacific: Definition Comparison and Normal- and Shear-Strain Decomposition

The spectral kinetic-energy flux is an effective tool to analyze the kinetic-energy transfer across a range of length scales, also known as the kinetic-energy cascade. Three methods to calculate spectral energy fluxes have been widely used, hereafter the ΠA, ΠF, and ΠQ definitions. However, the relations among these three definitions have not been examined in detail. Moreover, the respective contribution of the normal strain and shear strain of the flow field to kinetic-energy cascade has not been estimated before. Here, we use the kinetic energy equations to rigorously compare these definitions. Then, we evaluate the spectral energy fluxes, as well as its decomposition into the normal-strain and shear-strain components for the North Pacific, using a dynamically consistent global eddying state estimate. We find that the data must be preprocessed first to obtain stable results from the ΠF and ΠQ definitions, but not for the ΠA definition. For the upper 500 m of the North Pacific, in the wavenumber ranges with inverse kinetic-energy cascade, both the normal and shear-strain flow components contribute significantly to the spectral energy fluxes. However, at high wavenumbers, the dominant contributor to forward kinetic-energy cascade is the normal-strain component. These results should help shed light on the underlying mechanism of inverse and forward energy cascades.

Horizontal Stirring Over the Northeast U.S. Continental Shelf: The Spatial and Temporal Evolution of Surface Eddy Kinetic Energy

AbstractThis study examines the spatial and temporal variability of eddy kinetic energy over the Northeast Shelf using observations of surface currents from a unique array of six high frequency radar systems. Collected during summer and winter conditions over three consecutive years, the horizontal scales present were examined in the context of local wind and hydrographic variability, which were sampled concurrently from moorings and autonomous surface vehicles. While area‐averaged mean kinetic energy at the surface was tightly coupled to wind forcing, eddy kinetic energy was not, and was lower in magnitude in winter than summer in all areas. Kinetic energy wavenumber spectral slopes were generally near k−5/3, but varied seasonally, spatially, and between years. In contrast, wavenumber spectra of surface temperature and salinity along repeat transect lines had sharp k−3 spectral slopes with little seasonal or inter‐annual variability. Radar‐based estimates of spectral kinetic energy fluxes revealed a mean transition scale of energy near 18 km during stratified months, but suggested much longer scales during winter. Overall, eddy kinetic energy was unrelated to local winds, but the up‐ or down‐scale flux of kinetic energy was tied to wind events and, more weakly, to local density gradients.

Non-equilibrium mid-infrared black phosphorus light emitter and absorber for thermophotonic applications

A non-equilibrium mid-infrared black phosphorus (BP) light emitter and absorber for a thermophotonic (TPX) system was investigated in this study. A fluctuational electromagnetic simulation was performed to evaluate the non-equilibrium spectral energy fluxes from the bulk BP and between the bulk BPs, and the calculated spectral energy flux of the BP emitter exceeded the blackbody limit. The underlying resonant mechanisms were discovered by examining the dispersion relation and the gap transition from the near-field to the far-field of the transmission factor. The electric power generation and efficiency of the TPX system utilizing BP emitter and absorber were calculated and discussed. The results of this study are useful for not only fundamental energy-transfer research but also efficient heat energy recovery via TPX power-generation systems.

Numerical study of radiating xenon plasma

In this paper numerical simulation of the spectral properties of xenon plasma is carried out for various parameters (temperature, density, pressure) within the framework of the Saha-Boltzmann approximation. For calculations, pre-prepared atomic databases with varying degrees of detail of ion states were used. The effect of ionization potential depression was taken into account. The spectral absorption coefficients and emissivity, as well as the spectral radiation energy flux for a homogeneous plasma in a spherically symmetric geometry, were obtained. The identification of strong spectral lines in the wavelength ranges of interest has been carried out.

Shell model of turbulent viscosity for the boundary layer

The problem of numerical simulation of developed turbulent flows is usually reduced to the choice of one or another closure of the mean field equations. It is hardly possible to find a universal solution to this issue; nevertheless, the development of an approach based on general principles remains an active research topic. This paper proposes a model of turbulent viscosity described in terms of the characteristics of velocity field fluctuations calculated on the basis of shell models. These models reproduce correctly the scale distribution of the turbulent energy and the spectral energy fluxes for hydrodynamic flows of various physical nature. Shell models are constructed using symmetry properties and conservation laws of the complete system of equations, as well as an assumption on homogeneity and isotropy of turbulence. Phenomenological relations implying specific spectral laws are not involved. In the developed approach, we did an attempt to determine the turbulent viscosity, while maintaining the universality and flexibility of shell models. The resulting mathematical formulation is a set of models for large (mean field equation) and small (cascade model) scales, as well as closing relations. The model implements energy conjugation of variables of different scales, which provides a nonlinear relation of fields at different levels. Taking into account the influence of the mean field on the energy distribution of turbulent fluctuations is a distinctive feature of the proposed approach. Numerical solutions are obtained for the flow in a plane infinite channel at various Reynolds numbers. It is shown that the obtained results are consistent with modern concepts of the logarithmic profile of the velocity field in the boundary layer. The physical meaning of model parameters is substantiated. Asymptotic solutions that qualitatively correspond to the Prandtl model are found.

A connection between spectral sharpness and energies as well as flux in fermi gamma-ray bursts

ABSTRACT We revisit the sharpness angle (θ) under the peak or break of gamma-ray burst (GRB) spectra with the best peak flux P and time-integrated F spectral data provided by the Fermi GBM Burst Catalogue. We compute the sharpness angles of best-fit model spectra and check some interesting relations between θ and physics quantities. It is found that (i) a positive correlations between θ and the observed fluence as well as the isotropic radiated energy holds among GRBs, especially for the F spectra; (ii) when checking the correlation between θ and energy flux a weaker anti-correlation holds among GRBs and a tighter anti-correlation holds within GRBs, especially in single pulses. Our results further show that the spectral shape is related to the energy and flux by cross-checking other measures of spectral curvature. The correlated relationship between spectral sharpness and energy flux can be well explained as a thermal origin for GRB prompt emission: A large entropy around the peak of the light curve makes the photosphere approach the saturation radius, resulting in an intense emission with a narrow spectrum; as the entropy decreases, the photosphere deviates from the saturation radius, resulting in weaker emission with a broader spectrum.

Energy Sources Generation and Energy Cascades along the Kuroshio East of Taiwan Island and the East China Sea

There are multi-spatial-scale ocean dynamic processes in the western boundary current region, so the budget of energy source and sink in the Kuroshio Current area can describe the oceanic energy cycle and transformation more accurately. The slope of the one-dimensional spectral energy density varies between −5/3 and −3 in the wavenumber range of 0.02–0.1 cpkm, indicating an inverse energy cascade in the Kuroshio of Taiwan Island and the East China Sea. According to the steady-state energy evolution, an energy source must be present. The locations of energy sources were identified using the spectral energy transfer calculated by 24 years of Ocean General Circulation Model for the Earth Simulator (OFES) data. At the sea surface, the kinetic energy (KE) sources are mainly within 23.2°–25.6° Nand 28°–29° N at less than 0.02 cpkm and within 23.2°–25° N and 26°–30° N at 0.02–0.1 cpkm. The available potential energy (APE) sources are mainly within 22°–28° N and 28.6°–30° N at less than 0.02 cpkm and within 22.6°–24.6° N, 25.4°–28° N and 29.2°–30° N at 0.02–0.1 cpkm. Beneath the sea surface, the energy sources are mainly above 400 m depth. Wind stress and density differences are primarily responsible for the KE and APE sources, respectively. Once an energy source is formed, to maintain a steady state, energy cascades (mainly inverse cascades by calculating spectral energy flux) will be engendered. By calculating the energy flux at 600 m depth, KE changes from inflow (sink) to outflow (source), and the conversion depth of source and sink is 380 m. However, outflow of the APE behaves as the source.

Objective Assessment of Porcine Voice Acoustics for Laryngeal Surgical Modeling

Pigs have become important animal models in voice research. Several objective parameters exist to characterize the pig voice, but it is not clear which of them are sensitive to the impaired voice quality after laryngeal injury or surgery. In order to conduct meaningful voice research in pigs, it is critical to have standard functional voice outcome measures that can distinguish between normal and impaired voices. For this reason, we investigated 17 acoustic parameters before and early after surgery in three Yucatan mini pigs. Four parameters showed consistent changes between pre- and post-surgery recordings, mostly related to decreased spectral energy in higher frequencies after surgery. We recommend two of these, 50% spectral energy quartile (Q50) and Flux, for objective functional voice assessment of pigs undergoing laryngeal surgery. The long-term goal of this process is to enable quantitative voice outcome tracking of laryngeal surgical interventions in porcine models.

Wave Dissipation by Bottom Friction on the Inner Shelf of a Rocky Shore

AbstractApproximately 32% of the measured wave energy flux by sea and swell waves was dissipated over distances less than 130 m, outside of wave breaking on the inner shelf, over a rocky shore in southern Monterey Bay, CA. The bottom roughness of the rocky shore is defined by the standard deviation of bottom vertical variability, σb, that is 0.9 m, which is of similar magnitude to previously measured σb for rough coral reefs. Spectral wave energy flux balanced by bottom friction is modeled and compared with observations. Measured average wave reflection was 0.08 and is neglected in the model. The average energy dissipation owing to bottom friction over the rocky shore results in energy friction factors, fe, ranging 4 to 34. The observed fe are larger than previously measured fe on coral reefs. An empirical power law relationship is developed for fe as a function of the ratio of wave orbital excursion amplitude, Ab, and σb, based on combined data from coral reefs, rocky platforms, and this rocky shore. As σb increases, fe increases. Numerical simulation by Yu et al. (2018, https://doi.org/10.9753/icce.v36.waves.57) of waves over large bottom variations, similar to observed on coral reefs, suggests that drag forces do not account for the large observed fe. Therefore, it is hypothesized that bottom friction on rocky shores is a function of multiscale physical and biological roughness.

Prandtl number dependence of stratified turbulence

Abstract

The Phillips spectrum and a model of wind-wave dissipation

We consider an extension of the kinetic equation developed by Newell & Zakharov (A.C. Newell and V.E. Zakharov. The role of the generalized Phillips' spectrum in wave turbulence. Phys.Lett.A, 372:4230-4233, 2008). The new equation takes into account not only the resonant four-wave interactions but also the dissipation associated with the wave breaking. A dissipation function that depends on the spectral energy flux is introduced into the equation. This function is determined up to a functional parameter, which optimal choice should be made based on comparison with the experiment. A kinetic equation with this dissipation function describes the transition from the Kolmogorov-Zakharov spectrum to the Phillips spectrum usually observed experimentally. The version of the dissipation function expressed in terms of the energy spectrum can be used for wave modeling and prediction of sea waves.

Global climate modeling of Saturn's atmosphere. Part III: Global statistical picture of zonostrophic turbulence in high-resolution 3D-turbulent simulations

We conduct an in-depth analysis of statistical flow properties calculated from the reference high-resolution Saturn simulation obtained by global climate modelling in Part II. In the steady state of this reference simulation, strongly energetic, zonally dominated, large-scale structures emerge, which scale with the Rhines scale. Spectral analysis reveals a strong anisotropy in the kinetic energy spectra, consistent with the zonostrophic turbulent flow regime. By computing spectral energy and enstrophy fluxes we confirm the existence of a double cascade scenario related to 2D-turbulent theory. To diagnose the relevant 3D dynamical mechanisms in Saturn's turbulent atmosphere, we run a set of four simulations using an idealized version of our Global Climate Model devoid of radiative transfer, with a well-defined Taylor-Green forcing and over several rotation rates (4, 1, 0.5, and 0.25 times Saturn's rotation rate). This allows us to identify dynamics in three distinctive inertial ranges: (1) a “residual-dominated” range, in which non-axisymmetric structures dominate with a −5/3 spectral slope; (2) a “zonostrophic inertial” range, dominated by axisymmetric jets and characterized by the pile-up of strong zonal modes with a steeper, nearly −3, spectral slope; and (3) a “large-scale” range, beyond Rhines' typical length scale, in which the reference Saturn simulation and our idealized simulations differ. In the latter range, the dynamics is dominated by long-lived zonal modes 2 and 3 when a Saturn-like seasonal forcing is considered (reference simulation), and a steep energetic decrease with the idealized Taylor-Green forcing. Finally, instantaneous spectral fluxes show the coexistence of upscale and downscale enstrophy/energy transfers at large scales, specific to the regime of zonostrophic turbulence in a 3D atmosphere.

Global climate modeling of Saturn's atmosphere. Part III: Global statistical picture of zonostrophic turbulence in high-resolution 3D-turbulent simulations

We conduct an in-depth analysis of statistical flow properties calculated from the reference high-resolution Saturn simulation obtained by global climate modelling in Part II. In the steady state of this reference simulation, strongly energetic, zonally dominated, large-scale structures emerge, which scale with the Rhines scale. Spectral analysis reveals a strong anisotropy in the kinetic energy spectra, consistent with the zonostrophic turbulent flow regime. By computing spectral energy and enstrophy fluxes we confirm the existence of a double cascade scenario related to 2D-turbulent theory. To diagnose the relevant 3D dynamical mechanisms in Saturn's turbulent atmosphere, we run a set of four simulations using an idealized version of our Global Climate Model devoid of radiative transfer, with a well-defined Taylor-Green forcing and over several rotation rates (4, 1, 0.5, and 0.25 times Saturn's rotation rate). This allows us to identify dynamics in three distinctive inertial ranges: (1) a ``residual-dominated'' range, in which non-axisymmetric structures dominate with a -5/3 spectral slope; (2) a ``zonostrophic inertial'' range, dominated by axisymmetric jets and characterized by the pile-up of strong zonal modes with a steeper, nearly -3, spectral slope; and (3) a ``large-scale'' range, beyond Rhines' typical length scale, in which the reference Saturn simulation and our idealized simulations differ. In the latter range, the dynamics is dominated by long-lived zonal modes 2 and 3 when a Saturn-like seasonal forcing is considered (reference simulation), and a steep energetic decrease with the idealized Taylor-Green forcing. Finally, instantaneous spectral fluxes show the coexistence of upscale and downscale enstrophy/energy transfers at large scales, specific to the regime of zonostrophic turbulence in a 3D atmosphere.

Energy Spectrum of Turbulent Velocity Pulsations at Arbitrary Values of Fluid Viscosity

The problem of calculating the energy spectrum of turbulent velocity pulsations in the case of homogeneous isotropic and stationary turbulence is considered. The domain of turbulent energy production is treated as “a black box” on which boundary the spectral energy flux is given. It is assumed that the spectrum is formatted due to intermodal interactions being local in the wave-number space that leads to a cascade mechanism of energy transfer along the wave-number spectrum and the possibility of using the renormalization-group method related to the Markovian features of the process under consideration. The obtained formula for energy spectrum is valid in a wide wave-number range and at arbitrary values of fluid viscosity. It is shown that in functional formulation of the statistical theory of turbulence, the procedure of separating local intermodal interactions, which govern energy transfer (straining effect), and filtering out nonlocal interactions, which have no influence on energy transfer (sweeping effect), is directly described without providing additional arguments or conjectures commonly used in the renormalization-group analysis of turbulent spectra.

Partial Invariants, Large-scale Dynamo Action, and the Inverse Transfer of Magnetic Helicity

The existence of partially conserved enstrophy-like quantities is conjectured to cause inverse energy transfers to develop embedded in magnetohydrodynamical (MHD) turbulence, in analogy to the influence of enstrophy in two-dimensional nonconducting turbulence. By decomposing the velocity and magnetic fields in spectral space onto helical modes, we identify subsets of three-wave (triad) interactions conserving two new enstrophy-like quantities which can be mapped to triad interactions recently identified with facilitating large-scale $\alpha$-type dynamo action and the inverse transfer of magnetic helicity. Due to their dependence on interaction scale locality, the invariants suggest that the inverse transfer of magnetic helicity might be facilitated by both local- and nonlocal-scale interactions, and is a process more local than the $\alpha$-dynamo. We test the predicted embedded (partial) energy fluxes by constructing a shell model (reduced wave-space model) of the minimal set of triad interactions (MTI) required to conserve the ideal MHD invariants. Numerically simulated MTIs demonstrate that, for a range of forcing configurations, the partial invariants are, with some exceptions, indeed useful for understanding the embedded contributions to the total spectral energy flux. Furthermore, we demonstrate that strictly inverse energy transfers may develop if enstrophy-like conserving interactions are favoured, a mechanism recently attributed to the energy cascade reversals found in nonconducting three-dimensional turbulence subject to strong rotation or confinement. The presented results have implications for the understanding of the physical mechanisms behind large-scale dynamo action and the inverse transfer of magnetic helicity, processes thought to be central to large-scale magnetic structure formation.

The Effect of Measurement Limitations on High-Frequency Radar-Derived Spectral Energy Fluxes

AbstractThe ocean’s inverse cascade of energy from small to large scales has been confirmed from satellite altimetry for scales larger than 100 km. However, measurements of the direct energy cascade to smaller scales have remained difficult to obtain. Here, the possibility of estimating these energy transfers to smaller scales from observations by high-frequency radars is investigated using numerical simulations. Synthetic measurements are first extracted from a quasigeostrophic simulation of freely decaying turbulence for which the reference energy flux is characterized by the transition from positive to negative values. Fluxes obtained from synthetic data are compared to this reference flux in order to assess the robustness to various measurement limitations. The geometry of the observational domain (nonperiodicity, domain size, and aspect ratio) affects mostly large scales, while the spatial resolution of the instruments affects mostly small scales. In contrast, measurement noise and missing data affect both large and small scales. Despite resulting in significant biases in the amplitude of the fluxes, the transition scale between the positive and negative fluxes is relatively robust to measurement limitations. These results are also confirmed using a simulation from a primitive-equations model in a realistic coastal geometry.